scholarly journals On the Error Rate Comparison of the Quadratic Discriminant Function, Euclidean Distance Classifier, Fisher’s Linear Discriminant Function and the Vine Copulas

2018 ◽  
Vol 8 (1) ◽  
pp. 113
Author(s):  
A. Nanthakumar
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Euclidean Distance ◽  
Error Rates ◽  
Linear Discriminant Function ◽  
Misclassification Error ◽  
Classification Problems ◽  
Linear Discriminant ◽  
Quadratic Discriminant Function ◽  
Vine Copulas

The estimation of the error rates is of vital importance in classification problems as this is used as a basis to choose the best discriminant function; that is, the one with a minimum misclassification error. The quadratic discriminant function (QDF), Euclidean Distance Classifier (EDC), and Fisher’s Linear Discriminant Function (FLDC) have been in use for a long time for the purpose of classification. In this paper, we compare the misclassification error rate of the QDF, EDC, and FLDC with the Vine Copulas based on Gaussian and Clayton models. The results were obtained for the general case where the means are unequal and the covariance matrices are unequal.

The Performance of the Linear Discriminant Function in Nonoptimal Situations and the Estimation of Classification Error Rates: A Review of Recent Findings

1979 ◽  
Vol 16 (3) ◽  
pp. 370-381 ◽  
Author(s):  
William R. Dillon
Keyword(s):  
Discriminant Function ◽  
Error Rates ◽  
Linear Discriminant Function ◽  
Alternative Methods ◽  
Misclassification Error ◽  
Practical Significance ◽  
Classification Error ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Linear Discriminant

This article is a review of the results, as are available, on the performance of the linear discriminant function in situations where the assumptions of multivariate normality and equal group dispersion structures are violated. Some new results are discussed for the case of classification using discrete variables, and in the case of both binary and continuous variables. In addition, alternative methods which have been proposed, and evaluated, for estimating misclassification error rates are thoroughly reviewed. In all cases, the material is reviewed in terms of practical significance, with particular emphasis on the conditions unfavorable to the performance of each procedure.

scholarly journals Classification of all-rounders in limited over cricket - a machine learning approach

2021 ◽  
Vol 6 (4) ◽  
pp. 295-306
Author(s):  
Ananda B. W. Manage ◽  
Ram C. Kafle ◽  
Danush K. Wijekularathna
Keyword(s):  
Machine Learning ◽  
Support Vector Machine ◽  
Logistic Regression ◽  
Discriminant Function ◽  
Linear Discriminant Function ◽  
Classification Rule ◽  
Support Vector ◽  
Classification Methods ◽  
Linear Discriminant ◽  
Quadratic Discriminant Function

In cricket, all-rounders play an important role. A good all-rounder should be able to contribute to the team by both bat and ball as needed. However, these players still have their dominant role by which we categorize them as batting all-rounders or bowling all-rounders. Current practice is to do so by mostly subjective methods. In this study, the authors have explored different machine learning techniques to classify all-rounders into bowling all-rounders or batting all-rounders based on their observed performance statistics. In particular, logistic regression, linear discriminant function, quadratic discriminant function, naïve Bayes, support vector machine, and random forest classification methods were explored. Evaluation of the performance of the classification methods was done using the metrics accuracy and area under the ROC curve. While all the six methods performed well, logistic regression, linear discriminant function, quadratic discriminant function, and support vector machine showed outstanding performance suggesting that these methods can be used to develop an automated classification rule to classify all-rounders in cricket. Given the rising popularity of cricket, and the increasing revenue generated by the sport, the use of such a prediction tool could be of tremendous benefit to decision-makers in cricket.

scholarly journals Performance of Robust Linear Classifier with Multivariate Binary Variables

2015 ◽  
Vol 7 (4) ◽  
pp. 104
Author(s):  
I. Egbo ◽  
M. Egbo ◽  
S. I. Onyeagu
Keyword(s):  
Maximum Likelihood ◽  
Discriminant Function ◽  
Likelihood Function ◽  
Error Rates ◽  
Linear Discriminant Function ◽  
Data Set ◽  
Binary Variables ◽  
Linear Discriminant ◽  
Linear Classifiers ◽  
Fisher’S Linear Discriminant

<p>This paper focuses on the robust classification procedures in two group discriminant analysis with multivariate binary variables. A normal distribution based data set is generated using the R-software statistical analysis system 2.15.3 using Barlett’s approximation to chi-square, the data set was found to be homogenous and was subjected to five linear classifiers namely: maximum likelihood discriminant function, fisher’s linear discriminant function, likelihood ratio function, full multinomial function and nearest neighbour function rule. To judge the performance of these procedures, the apparent error rates for each procedure are obtained for different sample sizes. The results obtained ranked the procedures as follows: fisher’s linear discriminant function, maximum likelihood, full multinomial, likelihood function and nearest neigbour function.</p>

scholarly journals Annotations on the Relationship Among Discriminant Functions

2020 ◽  
pp. 161-165
Author(s):  
Awogbemi Clement Adeyeye
Keyword(s):  
Linear Relationship ◽  
Discriminant Function ◽  
Dimensional Space ◽  
Discriminant Functions ◽  
Classification Problems ◽  
Linear Discriminant ◽  
Equal Variance ◽  
Quadratic Discriminant Function ◽  
Higher Dimensional ◽  
The Relationship

Different forms of discriminant functions and the essence of their appearances were considered in this study. Various forms of classification problems were also considered, and in each of the cases mentioned, classification from simple functions of the observational vector rather than complicated regions in the higher-dimensional space of the original vector were made. Violation of condition of equal variance covariance matrix for Linear Discriminant Function (LDF) results to Quadratic Discriminant Function (QDF). The relationships among the classification statistics examined were established: The Anderson’s (W) and Rao’s (R) statistics are equivalent when the two sample sizes are equal, and when a constant is equal to 1, W, R and John-Kudo’s (Z) classification statistics are asymptotically comparable. A linear relationship is also established between W and Z classification statistics.

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